Topicme01210373f597a70_1528449000663_0Topic

Volume of the cylinder

Levelme01210373f597a70_1528449084556_0Level

Third

Core curriculumme01210373f597a70_1528449076687_0Core curriculum

X. Solid geometry (Stereometry). The student:

6) calculates the volume and surface area of prisms, pyramids, cylinder, cone, ball, also using trigonometry and the theorems learned.

Timingme01210373f597a70_1528449068082_0Timing

45 minutes

General objectiveme01210373f597a70_1528449523725_0General objective

Applying mathematical objects and manipulating them, interpreting mathematical concepts.

Specific objectivesme01210373f597a70_1528449552113_0Specific objectives

1. Calculation of the volume of the cylinder

2. Communicating in English, developing competences in mathematics, science, technology and IT, developing learning skills.

Learning outcomesme01210373f597a70_1528450430307_0Learning outcomes

The student:

- calculates the volume of the cylinder.

Methodsme01210373f597a70_1528449534267_0Methods

1. Discussion.

2. Situational analysis.

Forms of workme01210373f597a70_1528449514617_0Forms of work

1. Work in pairs.

2. Group work.

Lesson stages

Introductionme01210373f597a70_1528450127855_0Introduction

The teacher informs the students that during the lesson they will calculate the volume of the cylinder.

Procedureme01210373f597a70_1528446435040_0Procedure

Discussion - How to calculate the amount of water to fill the cylindrical glass?me01210373f597a70_1527752256679_0How to calculate the amount of water to fill the cylindrical glass?

Students consider the problem by approximation of the prism to the cylinder model. They create a hypothesis and verify it against available sources of information - for example on the Internet. They form a formula for the volume of the cylinder.

Conclusion
The volume V of the cylinder with the radius of the base r is equal to the product of the base area PIndeks dolny b_b of the cylinder by its height H.me01210373f597a70_1527752263647_0The volume V of the cylinder with the radius of the base r is equal to the product of the base area PIndeks dolny b_b of the cylinder by its height H.

$V=P_b·H$

$V={\mathrm{\pi r}}^2·H$

[Geogebra applet]

Students work individually using computers. Their task is to calculate the surface area and volume of the cylinder.

Students use acquired knowledge to solve word problems.

Task 1
[Illustration 1]

Calculate the volume of each of the cylinders shown in the figure.

Task 2
What is the volume of a cylinder whose diagonal of the axial section has a length of $4\sqrt{2}$, and the diameter of the base is equal to the height of the cylinder?

Task 3
The axial section of the cylinder is a rectangle in which one of the sides, equal to the diameter of the cylinder, is twice as long as the other side. Calculate the volume of this cylinder if its surface area is equal to $16\mathrm{\pi }$ cmIndeks górny 2².

Task 4
Can you fit 4 litres of paint in a can of the shape of a cylinder with a diameter of 20 cm and a height of 30 cm?

Task for volunteers
In a cylinder with a height of 30 cm and a diameter of the base 26 cm, a cylindrical whole was drilled in the middle with the radius of 4 cm. What volume does the resulting solid have?

Lesson summaryme01210373f597a70_1528450119332_0Lesson summary

Students do additional exercises.
Then they summarize the lesson together, formulating the conclusion to remember.

The volume V of the cylinder with the radius of the base r is equal to the product of the PIndeks dolny p_p base area of the cylinder by its height H.me01210373f597a70_1527752263647_0The volume V of the cylinder with the radius of the base r is equal to the product of the PIndeks dolny p_p base area of the cylinder by its height H.

$V=P_b·H$

$V={\mathrm{\pi r}}^2·H$

Selected words and expressions used in the lesson plan

base areabase areabase area

cylindercylindercylinder

cylinder basecylinder basecylinder base

cylinder heightcylinder heightcylinder height

cylinder netcylinder netcylinder net

cylinder surface areacylinder surface areacylinder surface area

cylinder volumecylinder volumecylinder volume